
theorem
for F being Field,
    E being (Polynom-Ring F)-homomorphic FieldExtension of F
for a being F-algebraic Element of E
holds (Polynom-Ring F)/({MinPoly(a,F)}-Ideal), FAdj(F,{a}) are_isomorphic
proof
let F be Field, E be (Polynom-Ring F)-homomorphic FieldExtension of F;
let a be F-algebraic Element of E;
set f = hom_Ext_eval(a,F);
(Polynom-Ring F)/(ker f), Image f are_isomorphic by RING_2:15;
then (Polynom-Ring F)/({MinPoly(a,F)}-Ideal), Image f are_isomorphic by mpol1;
then (Polynom-Ring F)/({MinPoly(a,F)}-Ideal), RAdj(F,{a}) are_isomorphic
  by lemphi4;
hence thesis by ch1;
end;
